arXiv subjects

Remi Rhodes

Publications and source records attributed to Remi Rhodes.

3 recordsLinked to original sources

arXiv2025

Probabilistic construction of non compactified imaginary Liouville field theory

We propose a probabilistic construction of imaginary Liouville Field Theory based on a real (non-compactified) Gaussian Free Field. We argue that our theory is the first explicit Lagrangian field theory that reproduces the imaginary DOZZ structure constants without requiring a neutrality constraint. Our proposal is supported by exact results for the imaginary Gaussian Multiplicative Chaos on the circle, and by numerical simulations on the sphere. In particular, we show that the three-point functions of the theory agree remarkably well with the imaginary DOZZ structure constants.

hep-th↗

arXiv2009

Stochastic Homogenization of Reflected Diffusion Processes

We investigate a functional limit theorem (homogenization) for Reflected Stochastic Differential Equations on a half-plane with stationary coefficients when it is necessary to analyze both the effective Brownian motion and the effective local time. We prove that the limiting process is a reflected non-standard Brownian motion. Beyond the result, this problem is known as a prototype of non-translation invariant problem making the usual method of the "environment as seen from the particle" inefficient.

math.PR↗

arXiv2008

Scaling limits for symmetric Ito-Levy processes in random medium

We are concerned with scaling limits of the solutions to stochastic differential equations with stationary coefficients driven by Poisson random measures and Brownian motions. We state an annealed convergence theorem, in which the limit exhibits a diffusive or superdiffusive behavior, depending on the integrability properties of the Poisson random measure

math.PR↗